How to Calculate the Empirical Formula from Experimental Data

If you can calculate the empirical formula from experimental data, you'll be able to handle a common chemistry exam question. This lesson shows you the key facts, the step-by-step method, exam traps to avoid, and gives you practice questions to test your skills.

Key Facts to Remember

• Empirical formula is the simplest whole-number ratio of atoms in a compound.
• You usually start with experimental data: the masses or percentages of each element in a sample.
• You need to convert these masses into moles, then find the simplest ratio.

Step-by-Step Method

1. Write down the mass (or percentage) of each element.

2. Convert the masses to moles by dividing by each element's relative atomic mass (Ar).

   $\text{Moles} = \frac{\text{mass (g)}}{\text{Ar}}$

3. Divide all mole values by the smallest number of moles to get a ratio.

4. If needed, multiply all ratios by a whole number to get the smallest whole numbers possible.

5. Write the empirical formula using these numbers as subscripts.

Worked Example

Question: A compound contains 2.40 g of magnesium and 1.60 g of oxygen. What is its empirical formula?

1. Write the masses:
   • Mg: 2.40 g
   • O: 1.60 g
2. Convert to moles:
   • Mg: $\frac{2.40}{24} = 0.10$ mol (Ar of Mg = 24)
   • O: $\frac{1.60}{16} = 0.10$ mol (Ar of O = 16)
3. Divide by smallest number of moles:
   • Mg: $0.10 / 0.10 = 1$
   • O: $0.10 / 0.10 = 1$
4. Empirical formula: MgO

Where Students Go Wrong

• Forgetting to use atomic masses (Ar): Always check the periodic table for correct values.
• Not dividing by the smallest mole value: This step is crucial for getting whole numbers.
• Leaving ratios as decimals: If you get 1:1.5, multiply both by 2 to get whole numbers (2:3).
• Mixing up empirical and molecular formula: Remember, empirical is the simplest ratio, not the actual number of atoms in a molecule.

Practice Questions

1. A compound contains 4.8 g of carbon and 1.6 g of hydrogen. Find its empirical formula. (Ar: C = 12, H = 1)
2. A sample contains 7.1 g of chlorine and 2.0 g of hydrogen. What is the empirical formula? (Ar: Cl = 35.5, H = 1)

Answers:

1. C: $4.8/12 = 0.4$; H: $1.6/1 = 1.6$; Ratio: $0.4:1.6 = 1:4$; Empirical formula: CH$_4$
2. Cl: $7.1/35.5 = 0.2$; H: $2.0/1 = 2.0$; Ratio: $0.2:2.0 = 1:10$; Empirical formula: H$_{10}$Cl

Takeaway

Practise this method until you can do it quickly and accurately. For more chemistry practice and guided lessons, you can sign up for free at TutorAI.